Diffusion in sheared athermal soft-particle suspensions: the role of inertia and dissipation mechanism

We perform numerical simulations to study diffusion in a model bi-disperse frictionless athermal soft-particle suspension of disks in two dimensions (2D). To model athermal shear, we damp the motion of a particle \emph{either} with respect to the globally imposed flow \emph{or} with respect to its near neighbors. We study shear flows at various rate $\dot{\gamma}$, system size $L$, and damping strength $b$ at packing fractions well above the random close packing point. At low $\dot{\gamma}$, we find a quasi-static effective transverse diffusion co-efficient, $D_{\rm eff}$, which has very weak dependence on $\phi$, $b$, or the damping mechanism yet has a pronounced linear dependence on $L$ in agreement with what is observed in conventional models of bulk metallic glasses. Away from the quasi-static regime, $D_{\rm eff}$ no longer depends on $L$, and $b$ has a profound impact on the scaling behavior of $D_{\rm eff}$ with $\dot{\gamma}$.